$C^{*}$-points vs $P$-points and $P^{♭}$-points

Martinez, Jorge, and McGovern, Warren Wm.. "$C^*$-points vs $P$-points and $P^\flat $-points." Commentationes Mathematicae Universitatis Carolinae 62 63.2 (2022): 245-259. <http://eudml.org/doc/298541>.

@article{Martinez2022,
abstract = {In a Tychonoff space $X$, the point $p\in X$ is called a $C^*$-point if every real-valued continuous function on $C\setminus \lbrace p\rbrace $ can be extended continuously to $p$. Every point in an extremally disconnected space is a $C^*$-point. A classic example is the space $\{\bf W\}^*=\omega _1+1$ consisting of the countable ordinals together with $\omega _1$. The point $\omega _1$ is known to be a $C^*$-point as well as a $P$-point. We supply a characterization of $C^*$-points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a $C^*$-point. This process leads to many interesting new discoveries.},
author = {Martinez, Jorge, McGovern, Warren Wm.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ring of continuous functions; $C^*$-embedded; $P$-point},
language = {eng},
number = {2},
pages = {245-259},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$C^*$-points vs $P$-points and $P^\flat $-points},
url = {http://eudml.org/doc/298541},
volume = {62 63},
year = {2022},
}

TY - JOUR
AU - Martinez, Jorge
AU - McGovern, Warren Wm.
TI - $C^*$-points vs $P$-points and $P^\flat $-points
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 2
SP - 245
EP - 259
AB - In a Tychonoff space $X$, the point $p\in X$ is called a $C^*$-point if every real-valued continuous function on $C\setminus \lbrace p\rbrace $ can be extended continuously to $p$. Every point in an extremally disconnected space is a $C^*$-point. A classic example is the space ${\bf W}^*=\omega _1+1$ consisting of the countable ordinals together with $\omega _1$. The point $\omega _1$ is known to be a $C^*$-point as well as a $P$-point. We supply a characterization of $C^*$-points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a $C^*$-point. This process leads to many interesting new discoveries.
LA - eng
KW - ring of continuous functions; $C^*$-embedded; $P$-point
UR - http://eudml.org/doc/298541
ER -